The Maximum Value Of The Expression 1 Sin 2 Theta 1) 2 2) 1 3) 3 4) 4 Answer: (1) 2 Solution: Let y = sin2θ + 3 sin θ cos θ + 5 cos2θ = (sin2θ + cos2θ) + (3/2) (2 sin θ cos θ) + 4... View Article
Let A B C Are The Angles Of A Plain Triangle And Tan A 2 1 3 1) 7/9 2) 2/9 3) 1/3 4) 2/3 Answer: (1) 7/9 Solution: Given, A, B and C are the angles of a plain triangle. Thus, A + B + C = π A/2 +... View Article
Cos 2theta Plus 2 Cos Theta Is Always 1) greater than -3/2 2) less than or equal to 3/2 3) greater than or equal to -3/2 and less than or equal to 3 4) None of these... View Article
The value of sin θ + cos θ will be greatest when 1) θ = 30° 2) θ = 45° 3) θ = 60° 4) θ = 90° Answer: (2) θ = 45° Solution: Let y = sin θ + cos θ Multiplying and dividing RHS by 2, y =... View Article
2 Sin 2 Beta 4 Cos Alpha Plus Beta Sin Alpha Sin Beta 1) sin 2α 2) cos 2β 3) cos 2α 4) sin 2β Answer: (3) cos 2α Solution: 2 sin2β + 4 cos (α + β) sin α sin β + cos 2(α + β) Using the formula... View Article
If Tan A Plus B P Tan A Minus B Q Then The Value Of Tan 2a 1) (p + q)/(p - q) 2) (p - q)/(1 + pq) 3) (p + q)/(1 - pq) 4) (1 + pq)/(1 - p) Answer: (3) (p + q)/(1 - pq) Solution: Given, tan(A... View Article
1 Plus Cos Pi 8 1 Plus Cos 3pi 8 1 Plus Cos 5pi 8 1) 1/2 2) 1/4 3) 1/8 4) 1/16 Answer: (3) 1/8 Solution: (1 + cos π/8)(1 + cos 3π/8)(1 + cos 5π/8)(1 + cos 7π/8) = (1 + cos π/8) [1... View Article
Sin 4 Pi 8 Plus Sin 4 3pi 8 Plus Sin 4 5pi 8 1) 1/2 2) 1/4 3) 3/2 4) 3/4 Answer: (3) 3/2 Solution: sin⁴(π/8) + sin⁴(3π/8) + sin⁴(5π/8) + sin⁴(7π/8) = [sin²(π/8)]² +... View Article
If Sin 6theta 32 Cos 5 Theta Sin Theta 32 Cos 3 Theta Sin Theta 1) cos θ 2) cos 2θ 3) sin θ 4) sin 2θ Answer: (4) sin 2θ Solution: Given, sin 6θ = 32 cos5θ sin θ - 32 cos3θ sin θ + 3x....(i) We... View Article
If X Cos Theta Y Cos Theta 2p 3 Z Cos Theta 2pi 3 Then 1) 1 2) 0 3) -1 4) None of these Answer: (2) 0 Solution: Given, x/cos θ = y/[cos(θ - 2π/3)] = z/[cos(θ + 2π/3)] Let x/cos θ =... View Article
If A Sin 2 X B Cos 2 X C B Sin 2 Y A Cos 2 Y And A Tan X 1) [(b - c)(d - b)]/ [(a - d)(c - a)] 2) [(a - d)(c - a)]/ [(b - c)(d - b)] 3) [(d - a)(c - a)]/ [(b - c)(d - b)] 4) [(b - c)(b - d)]/... View Article
If Cosec Theta P Plus Q P Minus Q Then 1) √(p/q) 2) √(q/p) 3) √pq 4) pq Answer: (2) √(q/p) Solution: Given, cosec θ = (p + q)/(p - q)....(i) 1/sin θ = (p + q)/(p - q)... View Article
If Tan X 2b A C A Not Equal To C Y A Cos 2 X 2b Sin X Cos X 1) y = z 2) y + z = a + c 3) y - z = a - c 4) y - z = (a - c)2 + 4b2 Answer: (3) y - z = a - c Solution: Given, tan x = 2b/(a -... View Article
If A Cos 2theta Plus B Sin 2theta C Has Alpha And Beta 1) (c + a)/2b 2) 2b/(c + a) 3) (c - a)/2b 4) b/(c + a) Answer: (2) 2b/(c + a) Solution: Given, a cos 2θ + b sin 2θ = c....(i)... View Article
If X Sin 130 Cos 80 Y Sin 80 Cos 130 Z 1 Xy Which One Of The Following Is True 1) x > 0, y > 0, z > 0 2) x > 0, y < 0, 0 < z < 1 3) x > 0, y < 0, z > 1 4) x < 0, y < 0, 0 < z... View Article
If A Plus C Equals To B Then Tan A Tan B Tan C 1) tan A tan B + tan C 2) tan B - tan C - tan A 3) tan A + tan C - tan B 4) -(tan A tan B + tan C) Answer: (2) tan B - tan C - tan A... View Article
Tan Alpha Plus 2 Tan 2alpha Plus 4 Tan 4 Alpha Plus 8 Cot 8alpha 1) tan α 2) tan 2α 3) cot α 4) cot 2α Answer: (3) cot α Solution: tan α + 2 tan 2α + 4 tan 4α + 8 cot 8α = tan α + 2 tan 2α + 4... View Article
The Value Of Sin Pi 14 Sin 3pi 14 Sin 5pi 14 Sin 7pi 14 1) 1/8 2) 1/16 3) 1/32 4) 1/64 Answer: (4) 1/64 Solution: sin π/14 sin 3π/14 sin 5π/14 sin 7π/14 sin 9π/14 sin 11π/14 sin 13π/14 =... View Article
If Cos Power 6 Alpha Sin Power 6 Alpha K Sin Square 2alpha 1) 4/3 2) 3/4 3) 1/2 4) 2 Answer: (2) 3/4 Solution: Given, cos6α + sin6α + K sin2(2α) = 1 (cos2α)3 + (sin2α)3 + K sin2(2α) = 1... View Article
If Tan Theta Equal To Sin Alpha Minus Cos Alpha 1) √2 cos θ, √2 sin θ 2) √2 sin θ, √2 cos θ 3) √2 sin θ, √2 sin θ 4) √2 cos θ, √2 cos θ Answer: (1) √2 cos θ, √2 sin θ Solution:... View Article
